The voltages at all buses in a power grid should be maintained within a specified operational range to ensure stable operation. The voltage at a node, which is called as a local variable, should be controlled by a generator or the reactive power compensating unit closest to the applicable node. For a grid with high wind penetration, wind power plants (WPPs) are required to have the capability to maintain the voltage at the point of common coupling (PCC). In order to maintain the PCC voltage within the acceptable ranges, the desired reactive power should be injected from a WPP. Wind generators in a WPP produce the different active power due to the wake effects and consequently contain different reactive power availability. This thesis proposes a voltage control scheme of a WPP using the adaptive reactive power-voltage (Q-V) characteristic of a doubly-fed induction generator (DFIG). The proposed scheme adjusts the Q-V gains of a DFIG depending on the operating condition to fully utilize the reactive power capability of the WPP. In order to stabilize the voltage of the PCC, the WPP controller calculates a voltage error signal using a PI controller, which is then sent to each DFIG. A DFIG injects the corresponding reactive power to the voltage error signal based on its Q-V characteristic, which depends on the operating condition of DFIGs so that the DFIGs with the higher reactive power capability might the inject more reactive power for the voltage recovery. The scheme enables the WPP to recover the PCC voltage to the nominal value within a short time after a disturbance by utilizing the available reactive power of a WPP. The performance of the scheme was investigated for a 100 MW WPP consisting of 20 units of a 5 MW DFIG under various wind conditions. The test results clearly indicate that the scheme successfully recovers the PCC voltage within a short time after disturbances.